Abstract Molecular dynamics simulations have been performed to study the rapid solidification processes of liquid Cu using different cooling rates ranging from 5 × 10 11 to 2 × 10 14 K/s. Based on the embedded-atom method (EAM), the time–temperature transformation (TTT) diagram is constructed. The critical cooling rate determined by the position of the nose of the diagram is suggested to be about 7 × 10 12 K/s. The radial distribution function (RDF) and the pair analysis (PA) results show that cooling the melt using a rate above the critical rate leads to a glass transition in the system. The glass transition temperature ( T g) increases with the increase of the cooling rate and can be well fitted by a Vogel–Fulcher-type function. There are large number of icosahedra and defect icosahedra in the glass system. They interact with each other and form large glass clusters during the cooling of the system. The size of the glass clusters grows rapidly until the liquid–solid transition temperature is reached. If the cooling rate is below the critical rate, crystallization happens. There are both fcc and hcp microstructures in the crystal Cu. The size of the critical nucleus is about 300 atoms, corresponding to a radius of about 10.4 Å when the cooling rate is 5 × 10 11 K/s. A higher cooling rate causes a smaller critical size and a faster growth rate of the nucleus.